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August 9, 2026European Journal of MathematicsOpen Access

A¹-homotopy theory of log schemes

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Authors

DPDoosung Park

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Overview

Randomized trial constructs A1-local stable homotopy categories for fs log schemes, suggesting new cohomology theories.

Key Points

  • The aim is to develop a stable motivic homotopy theory for fs log schemes and to prove that it satisfies the localization property.
  • Constructed A1-local stable motivic homotopy categories for fs log schemes.
  • Extended A1-invariant cohomology theories, including motivic cohomology and algebraic cobordism, to fs log schemes.
  • Formulated cohomology relations for the boundary of fs log schemes log smooth over a scheme.
  • Established that the new construction is equivalent to Morel–Voevodsky's for schemes with trivial log structure.
  • Satisfaction of the localization property has been proven in the context of fs log schemes.
  • Defined several cohomology theories, including homotopy K-theory for fs log schemes.

Cite This Study

Doosung Park (2026) studied this question.

synapsesocial.com/papers/6a782cb82e1896536c83f968https://doi.org/10.1007/s40879-026-00916-2
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